I think you mean "with ease" rather than "at ease". Otherwise it is OK, but I would be inclined to add commas to break it up for readability:

The way she switches to her younger voice with ease, and makes her voice sound the same as back in the 70s, proves yet again why she is a legend.

I prefer "70s" to "70's". Using apostrophes to indicate plurals is, generally speaking, horrible, so I prefer to avoid it unless it is absolutely necessary for intelligibility (e.g. plurals of letters).